Abstract
Original language  English 

Qualification  Doctor of Philosophy 
Awarding Institution 

Supervisors/Advisors 

Award date  28 Feb 2013 
Place of Publication  Eindhoven 
Publisher  
Print ISBNs  9789038633305 
DOIs  
Publication status  Published  2013 
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Multiscale reactiondiffusion systems describing concrete corrosion : modeling and analysis. / Fatima, T.
Eindhoven : Technische Universiteit Eindhoven, 2013. 174 p.Research output: Thesis › Phd Thesis 1 (Research TU/e / Graduation TU/e)
TY  THES
T1  Multiscale reactiondiffusion systems describing concrete corrosion : modeling and analysis
AU  Fatima, T.
PY  2013
Y1  2013
N2  This thesis deals with the modeling and multiscale analysis of reactiondiffusion systems describing concrete corrosion processes due to the aggressive chemical reactions occurring in concrete. We develop a mathematical framework that can be useful in forecasting the service life of sewer pipes. We aim at identifying reliable and easytouse multiscale models able to forecast the penetration of sulfuric acid into sewer pipes walls. For modeling of corrosion processes, we take into account balance equations expressing physicochemical processes that take place in the microstructures (pores) of the partially saturated concrete. We consider two dierent modeling strategies: (1) we propose microscopic reactiondiusion systems to delineate the corrosion processes at the pore level and (2) we consider a distributed microstructure model containing information from two separated spatial scales (micro and macro). All systems of dierential equations are semilinear, weakly coupled, and partially diusive. Since the precise microstructure of the material is far too complex to be described accurately, we consider two approximations, namely uniformlyperiodic and locallyperiodic array of microstructures, which are tractable by using averaging mathematical tools. We use different homogenization techniques to obtain the effective behavior of the microscopically oscillating quantities. For the formal derivation of our multiscale models, we apply the asymptotic expansion method to the microscopic reactiondiffusion systems defined in locallyperiodic domains for two special choices of scaling in ¿ of the diffusion coefficients. We end up with (i) upscaled systems and (ii) distributedmicrostructure systems. As far as rigorous derivations are concerned, we apply the notion of twoscale convergence to the PDE system defined in the uniformly periodic domain. To deal with the nondiffusive object, i.e. the ordinary dierential equation tracking the damagebyreaction, we combine the twoscale convergence idea with the periodicboundaryunfolding technique. Additionally, we use the periodic unfolding techniques to obtain corrector estimates assessing the quality of the averaging method. These estimates are convergence rates measuring the error contribution produced while approximating macroscopic solutions by microscopic ones. We derive these estimates under minimal regularity assumptions on the solutions to the microscopic and macroscopic systems, microstructure boundaries, and to the corresponding auxiliary cell problems. We prove the wellposedness of a distributedmicrostructure reactiondiusion system which includes transport (diusion) and reaction effects emerging from two separated spatial scales. We perform this analysis by incorporating a variational inequality requiring minimal regularity assumptions on the initial data. We ensure basic estimates like positivity and L8bounds on the solution to the system. Then we prove the globalintime existence and uniqueness of a suitable class of positive and bounded solutions. To predict the position of the corrosion front penetrating the concrete, we use our distributedmicrostructure model to perform simulations at macroscopic length scales while taking into account transport and reactions occurring at small length scales. Using an ad hoc logarithmic expression, we approximate numerically macroscopic pH proles dropping down with the onset of corrosion. We extract from the gypsum proles the approximate position of the corrosion front penetrating the uncorroded concrete. We illustrate numerically that as the macroscopic masstransfer Biot number BiM > 8, BiM naturally connects two different multiscale reactiondiusion scenarios: the solution of the distributedmicrostructure system having the Henry's law acting as micromacro transmission condition converges to the solution of the matched distributedmicrostructure system.
AB  This thesis deals with the modeling and multiscale analysis of reactiondiffusion systems describing concrete corrosion processes due to the aggressive chemical reactions occurring in concrete. We develop a mathematical framework that can be useful in forecasting the service life of sewer pipes. We aim at identifying reliable and easytouse multiscale models able to forecast the penetration of sulfuric acid into sewer pipes walls. For modeling of corrosion processes, we take into account balance equations expressing physicochemical processes that take place in the microstructures (pores) of the partially saturated concrete. We consider two dierent modeling strategies: (1) we propose microscopic reactiondiusion systems to delineate the corrosion processes at the pore level and (2) we consider a distributed microstructure model containing information from two separated spatial scales (micro and macro). All systems of dierential equations are semilinear, weakly coupled, and partially diusive. Since the precise microstructure of the material is far too complex to be described accurately, we consider two approximations, namely uniformlyperiodic and locallyperiodic array of microstructures, which are tractable by using averaging mathematical tools. We use different homogenization techniques to obtain the effective behavior of the microscopically oscillating quantities. For the formal derivation of our multiscale models, we apply the asymptotic expansion method to the microscopic reactiondiffusion systems defined in locallyperiodic domains for two special choices of scaling in ¿ of the diffusion coefficients. We end up with (i) upscaled systems and (ii) distributedmicrostructure systems. As far as rigorous derivations are concerned, we apply the notion of twoscale convergence to the PDE system defined in the uniformly periodic domain. To deal with the nondiffusive object, i.e. the ordinary dierential equation tracking the damagebyreaction, we combine the twoscale convergence idea with the periodicboundaryunfolding technique. Additionally, we use the periodic unfolding techniques to obtain corrector estimates assessing the quality of the averaging method. These estimates are convergence rates measuring the error contribution produced while approximating macroscopic solutions by microscopic ones. We derive these estimates under minimal regularity assumptions on the solutions to the microscopic and macroscopic systems, microstructure boundaries, and to the corresponding auxiliary cell problems. We prove the wellposedness of a distributedmicrostructure reactiondiusion system which includes transport (diusion) and reaction effects emerging from two separated spatial scales. We perform this analysis by incorporating a variational inequality requiring minimal regularity assumptions on the initial data. We ensure basic estimates like positivity and L8bounds on the solution to the system. Then we prove the globalintime existence and uniqueness of a suitable class of positive and bounded solutions. To predict the position of the corrosion front penetrating the concrete, we use our distributedmicrostructure model to perform simulations at macroscopic length scales while taking into account transport and reactions occurring at small length scales. Using an ad hoc logarithmic expression, we approximate numerically macroscopic pH proles dropping down with the onset of corrosion. We extract from the gypsum proles the approximate position of the corrosion front penetrating the uncorroded concrete. We illustrate numerically that as the macroscopic masstransfer Biot number BiM > 8, BiM naturally connects two different multiscale reactiondiusion scenarios: the solution of the distributedmicrostructure system having the Henry's law acting as micromacro transmission condition converges to the solution of the matched distributedmicrostructure system.
U2  10.6100/IR749279
DO  10.6100/IR749279
M3  Phd Thesis 1 (Research TU/e / Graduation TU/e)
SN  9789038633305
PB  Technische Universiteit Eindhoven
CY  Eindhoven
ER 